Thesis

Modelling volatilities of high-dimensional time series with network structure and asymmetry

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Awarding institution
  • University of Strathclyde
Date of award
  • 2024
Thesis identifier
  • T17147
Person Identifier (Local)
  • 201989614
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Department, School or Faculty
Abstract
  • This thesis explores innovative methodologies for modelling volatilities of network-based high-dimensional time series that exhibit asymmetry. We start with a law of large numbers and a central limit theorem for triangular arrays of random fields that are non-stationary. We derive key intermediate results to bridge the gap between the proposed limit theorems and their application to the inference of high-dimensional time series under large dimension N and sample size T. These theoretical advancements are exemplified through a maximum likelihood estimation of a network autoregressive model. Building on this foundation, we propose a threshold network GARCH (TNGARCH) model that incorporates asymmetries in the reaction of conditional variances to positive and negative shocks. Taking integer-valued data into account, we also propose a Poisson TNGARCH (PTNGARCH) model, which has an unknown threshold that can be estimated alongside other parameters. For both models, the stationarity over time is investigated, and the maximum likelihood estimation is proved to be consistent and asymptotically normal for large N and T. The asymptotic properties are tested by simulation studies. For real data analysis, we fit the TNGARCH model to the daily log-returns of stocks from two Chinese stock markets and the PTNGARCH model to the daily counts of car accidents in New York City neighbourhoods. Wald tests are conducted to show the asymmetry in both data sets. Additionally, we establish unified methodologies for a class of network GARCH models with conditional distributions in the one-parameter exponential family. This theoretical framework is applied to a new negative binomial TNGARCH model. We evaluate its performance against the Poisson TNGARCH model using the same car accident data, employing a probability integral transformation test for comparative analysis.
Advisor / supervisor
  • Pan, Jiazhu
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